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Prof. Dr. rer. nat. habil. Matthias Kriesell


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Veröffentlichungen am Institut für Mathematik seit 1990

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Eichfelder, Gabriele; Krüger, Corinna; Schöbel, Anita;
Decision uncertainty in multiobjective optimization. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (27 Seiten). . - (Preprint. - M16,06)

In many real-world optimization problems, a solution cannot be realized in practice exactly as computed, e.g., it may be impossible to produce a board of exactly 3.546˜mm width. Whenever computed solutions are not realized exactly but in a perturbed way, we speak of decision uncertainty. We study decision uncertainty in multiobjective optimization problems and we propose the concept decision robust efficiency for evaluating the robustness of a solution in this case. Therefore, we address decision uncertainty within the framework of set-valued maps. First, we prove that convexity and continuity are preserved by the resulting set-valued mappings. Second, we obtain specific results for particular classes of objective functions that are relevant for solving the set-valued problem. We furthermore prove that decision robust efficient solutions can be found by solving a deterministic problem in case of linear objective functions. We also investigate the relationship of the proposed concept to other concepts in the literature.
Leben, Leslie;
Non-negative operators in Krein spaces and rank one perturbations. - Ilmenau : Universitätsverlag Ilmenau, 2016. - Online-Ressource (116 Seiten, 6.65 MB).
Technische Universität Ilmenau, Dissertation 2016

In der vorliegenden Arbeit werden eindimensionale Störungen von nichtnegativen Operatoren in Kreinräumen betrachtet. Dabei wird untersucht wie sich die Anzahl der Eigenwerte und deren Vielfachheit in einer Lücke des essentiellen Spektrums unter einer Störung ändern können. Zudem wird beschrieben wie sich an einem Eigenwert die Anzahl und die Länge der linear unabhängigen Jordanketten ändern können.
Worthmann, Karl; Proch, Michael; Braun, Philipp; Schlüchtermann, Jörg; Pannek, Jürgen;
Towards dynamic contract extension in supplier development. - In: Logistics research. - Berlin : Springer, ISSN 1865-0368, Bd. 9.2016, Article 14, insg. 12 Seiten

We consider supplier development within a supply chain consisting of a single manufacturer and a single supplier. Because investments in supplier development are usually relationship-specific, safeguard mechanisms against the hazards of partner opportunism have to be installed. Here, formal contracts are considered as the primary measure to safeguard investments. However, formal contracts entail certain risks, e.g., a lack of flexibility, particular in an ambiguous environment. We propose a receding horizon control scheme to mitigate possible contractual drawbacks while significantly enhancing the supplier development process and, thus, to increase the overall supply chain profit. Our findings are validated by a numerical case study.
Fabrici, Igor; Harant, Jochen; Jendrol', Stanislav;
On longest cycles in essentially 4-connected planar graphs. - In: Discussiones mathematicae. - Warsaw : De Gruyter Open, ISSN 2083-5892, Bd. 36 (2016), 3, S. 565-575
Worthmann, Karl; Mehrez, Mohamed W.; Zanon, Mario; Mann, George K. I.; Gosine, Raymond G.; Diehl, Moritz;
Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs. - In: IEEE transactions on control systems technology : a publication of the IEEE Control Systems Society.. - New York, NY : IEEE, ISSN 1558-0865, Bd. 24 (2016), 4, S. 1394-1406
Hildenbrandt, Regina;
The k-server problem with parallel requests and the compound Harmonic algorithm. - In: Baltic journal of modern computing : BJMC.. - [S.l.], ISSN 2255-8950, Bd. 4 (2016), 3, S. 607-629

In this paper the (randomized) compound Harmonic algorithm for solving the generalized k-server problem is proposed. This problem is an online k-server problem with parallel requests where several servers can also be located on one point. In 2000 Bartal and Grove have proved that the well-known Harmonic algorithm is competitive for the (usual) k-server problem. Unfortunately, certain techniques of this proof cannot be used to show that a natural generalization of the Harmonic algorithm is competitive for the problem with parallel requests. The probabilities, which are used by the compound Harmonic algorithm are, finally, derived from a surrogate problem, where at most one server must be moved in servicing the request in each step. We can show that the compound Harmonic algorithm is competitive with the bound of the ratio as which has been proved by Bartal and Grove in the case of the usual problem.
Büttner, Florian; Trunk, Carsten;
Limit-point/limit-circle classification of second-order differential operators arising in PT quantum mechanics. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (6 Seiten). . - (Preprint. - M16,03)
Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten;
Bounds on the non-real spectrum of a singular indefinite Sturm-Liouville operator on R. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (4 Seiten). . - (Preprint. - M16,05)

A simple explicit bound on the absolute values of the non-real eigenvalues of a singular indefinite Sturm-Liouville operator on the real line with the weight function sgn(&hahog;) and an integrable, continuous potential q is obtained.
Gernandt, Hannes; Trunk, Carsten;
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (8 Seiten). . - (Preprint. - M16,04)

We study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only.
Ilchmann, Achim; Selig, Tilman; Trunk, Carsten;
The Byrnes-Isidori form for infinite-dimensional systems. - In: SIAM journal on control and optimization. - Philadelphia, Pa. : Soc., ISSN 1095-7138, Bd. 54 (2016), 3, S. 1504-1534